论文标题
关于圆锥线性编程问题的值函数的较低的半持续性和分别差异性
On the lower semicontinuity and subdifferentiability of the value function for conic linear programming problems
论文作者
论文摘要
纸张[N.E.的引理1 Gretsky，J.M。Ostroy，W.R。Zame，Subdferentibility and Duality Gap，阳性6：261---274，2002]断言，在标准形式的无限尺寸线性编程问题的值函数$ V $是标准形式的，每当$ v $适当的时间是较低的半连续性，并且适当的是适当的空间。在本说明中，人们表明，即使在有限维空间中，此陈述也是错误的，一个人提供了一个在希尔伯特空间中线性编程问题的示例，其（正确的）值函数在其域中的任何点（因此，它都不可分别）在其域中的任何点（因此它不可分割），一个人对其域名的限制在kretschmer的范围内，并在任何范围内都没有界限。在同一篇论文中。
Lemma 1 from the paper [N.E. Gretsky, J.M. Ostroy, W.R. Zame, Subdifferentiability and the duality gap, Positivity 6: 261--274, 2002] asserts that the value function $v$ of an infinite dimensional linear programming problem in standard form is lower semicontinuous whenever $v$ is proper and the involved spaces are normed vector spaces. In this note one shows that this statement is false even in finite-dimensional spaces, one provides an example of linear programming problem in Hilbert spaces whose (proper) value function is not lower semicontinuous (hence it is not subdifferentiable) at any point in its domain, one shows that the restriction of the value function to its domain in Kretschmer's gap example is not bounded on any neighborhood of any point of the domain, and discuss other assertions done in the same paper.
